Everything Maths Grade 12

CHAPTER 3. SEQUENCES AND SERIES 3.3

Extension: Plotting a graph of terms in an arithmetic sequence

Plotting a graph of theterms of a sequence sometimes helps in determining the type of se-

quence involved. For anarithmetic sequence, plotting anvs. n results in:

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gradient d

an= a 1 +d(n− 1)

Term:

a

n

y-intercept: a 1

Index: n

1 2 3 4 5 6 7 8 9

a 1

a 2

a 3

a 4

a 5

a 6

a 7

a 8

a 9

(Note that the graph will only be a straight line if the sequence is arithmetic.)

3.3 Geometric Sequences EMCQ

DEFINITION: Geometric Sequences

A geometric sequence is a sequence of numbers in which each new term (except for

the first term) is calculated by multiplying the previous term by aconstant value.

This means that the ratio between consecutive numbers in the geometricsequence is a constant.We

will explain what we mean by ratio after lookingat the following example.